Propagation of Intense Beams in Plasma

Abstract

When an intense charged particle beam is injected into a dense plasma, the beam space charge can be effectively neutralized by a redistribution of the plasma particles. For example, during injection of an intense electron beam, plasma electrons will move out of the beam region during the characteristic time (4πσ)⁻¹, which is typically quite short («10⁻⁹ sec). Hence, net space charge effects (e.g., radial expansion or virtual cathode formation) do not pose serious limitations to beam transport in a plasma. Another general limitation arises, however, from the constriction of the beam due to its azimuthal self-magnetic field. In the original analyses,¹ an upper limit for current propagation was derived as

$$ {{I}_{A}}\simeq {\beta \gamma m{{c}^{3}}}/{e}\; $$

(4.1)

where, as usual, β is the particle stream velocity divided by the velocity of light and γ=(1−β ²)^−1/2. I _A, the Alfven current limit, physically corresponds to the situation in which the beam self-magnetic field is sufficient to reverse the direction of the electron trajectories at the outer edge of the beam. In principle, this limitation can be avoided if the induced emf associated with the rising beam current is sufficient to drive a plasma current directed opposite to the beam current. Depending upon the plasma conductivity, the induction electric field can effectively cause the net current, and hence the magnetic field in the system, to vanish.